## Judita Cofman's books

 Judita Cofman wrote three books. Here we look at two of these, namely: What to solve? Problems and suggestions for young mathematicians (1990) and Numbers and shapes revisited. More problems for young mathematicians (1995). We give extracts from (A) the Preface, (B) the Acknowledgements, (C) Introduction to Chapter I, (D) Introduction to Chapter II, (E) Introduction to Chapter III, and (F) Introduction to Chapter IV of What to solve? at THIS LINK. Below we present extracts from reviews of the two works as well as some publisher's descriptions.

1. What to solve? Problems and suggestions for young mathematicians (1990), by Judita Cofman.
1.1. From the Publisher.

This book provides a wide variety of mathematical problems for teenagers and students to help stimulate interest in mathematical ideas outside of the classroom. Problems in the text vary in difficulty from the easy to the unsolved, but all will encourage independent investigation, demonstrate different approaches to problem-solving, and illustrate some of the famous dilemmas that well-known mathematicians have attempted to solve. Helpful hints and detailed discussions of solutions are included, making this book a valuable resource for schools, student teachers, and college mathematics courses, as well as for anyone fascinated by mathematical ideas.

1.2. Review by: John Baylis.
The Mathematical Gazette 75 (474) (1991), 473-474.

As the title modestly suggests, this is another book of problems and investigations suitable for the more gifted and enthusiastic pupils. What distinguishes it from most others in the field is that the problems have been tried out successfully over several years in the international camps for young mathematicians organised by Ms Cofman. .. I have been looking forward to this book ever since hearing Judita Cofman's talk on her mathematical camps at a Maths Association conference. I was not disappointed and I look forward to many more happy hours with the problems. Some have already figured in a course on proof and the book will continue to be well used. Highly recommended.

1.3. Review by: David M Neal.
Mathematics in School 20 (2) (1991), 47.

The subtitle, Problems and Suggestions for Young Mathematicians, provides a clearer description of this highly commendable book. There are many collections of mathematical problems for various ages and levels of ability so why commend another? The answer is simple. There are certain books that have proved of constant help to the secondary school teacher, not because they present a radical new set of ideas, but rather that they collect together the best of current thinking on a specific area of study and present it in a manner that provides the busy teacher with a long term reference of interesting and challenging material adaptable to the classroom. An example is Mathematical Models by Cundy and Rollitt, which has been used as a reference book by teachers for many years; this new book is another ... Those who have attended lectures given by Judita Cofman at conferences of the Mathematical Association, or who have experience of her work at Putney High School via Hypotenuse will be familiar with the quality of the challenging problems and the solutions and will be delighted with this book. Those who are unfamiliar will be rewarded as they study its content.

1.4. Review by: Leonard J Yutkins.
The Mathematics Teacher 84 (6) (1991), 496.

If you are interested in a source for problems for top high school students or first-year college students, this book is for you. The problems presented come from several problem seminars conducted by the author at international camps for young mathematicians. The students attending these camps ranged in age from thirteen to nineteen. The book is divided into four chapters reflecting the four stages of problem solving used at the camps, namely, (1) "encouraging in dependent investigation," (2) "demonstrating approaches to problem solving," (3) "discussing solutions of famous problems from past centuries," and (4) "describing questions considered by eminent contemporary mathematicians." The problems are well organized with excellent diagrams and complete solutions. The easier problems are designated by "(E)." The book is true to its title - problems and suggestions for young mathematicians.

2. Numbers and shapes revisited. More problems for young mathematicians (1995), by Judita Cofman.
2.1. From the Publisher.

Numbers and Shapes Revisited is the ideal guide for high school and undergraduate students seeking to understand the connections between the wide range of mathematical methods and concepts that they may come across in their curriculum. Topics include elementary number theory, classical algebra, euclidean geometry, group theory, and combinatorics. Stimulating and enjoyable, the book will promote independent thinking and the ability to pose and answer questions.

2.2. From the Preface.

[This book] intended for advanced secondary school pupils, aged fifteen and over, but it is hoped that undergraduates, students at teacher-training colleges, and mathematics teachers can also benefit from it.

2.3. From Booksellers.

Mathematics is primarily concerned with problem solving, and there is no better way of gaining an understanding of mathematics than by developing the independent thinking and ability to solve problems (and to set them). The mathematics syllabuses in today's secondary schools contain a wide range of notions and basic facts from various mathematical disciplines. Pupils interested in mathematics should be encouraged to explore the connections between the different topics they encounter, and this book attempts to help in pointing out these connections.

By focusing attention on the links between patterns of numbers and shapes, and on between algebraic relations and geometric and combinatorial configurations, the book aims to

(i) motivate deeper study of the concepts related to elementary mathematics,

(ii) emphasize the importance of the interrelations between mathematical phenomena,

(iii) foster the interplay of ideas involved in problem solving.

The material is presented in the form of problems and will prove invaluable and enjoyable for pupils, their teachers, and those studying mathematics or its teaching at university.

2.4. Review by: Phil Buckhiester.
The Mathematics Teacher 89 (6) (1996), 516.

This well-written book introduces various classical topics from number theory, real analysis, geometry, abstract algebra, and combinatorial analysis. Interrelations and connections are emphasized throughout. Part 1 presents each topic through a brief discussion followed by a sequence of problems. Some problems include hints and suggestions. The remainder of the book, approximately 60 per cent, presents solutions to the problems. Included are many proofs and derivations of formulas as well as investigation exercises. Some problems ask students to generalize, whereas others encourage them to explore special cases. The introductions to the topics are brief and, consequently, will re quire supplementary discussion and material. Some fairly sophisticated ideas are used in the solutions to the problems. ... Bright and highly motivated secondary school students will be challenged by the problems. Other precollege students are likely to find the material too difficult. The book could be a valuable reference for teachers of advanced secondary students and for teachers of undergraduate mathematics majors.

JOC/EFR August 2016